The elevation of boiling point of 0.10 m aqueous
Question: The elevation of boiling point of $0.10 \mathrm{~m}$ aqueous $\mathrm{CrCl}_{3} \cdot x \mathrm{NH}_{3}$ solution is two times that of $0.05 \mathrm{~m}$ aqueous $\mathrm{CaCl}_{2}$ solution. The value of $x$ is____________________ [Assume $100 \%$ ionisation of the complex and $\mathrm{CaCl}_{2}$, coordination number of $\mathrm{Cr}$ as 6 , and that all $\mathrm{NH}_{3}$ molecules are present inside the coordination sphere] Solution: (5.0)...
Read More →The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm.
Question: The osmotic pressure of a solution of $\mathrm{NaCl}$ is $0.10 \mathrm{~atm}$ and that of a glucose solution is $0.20$ atm. The osmotic pressure of a solution formed by mixing $1 \mathrm{~L}$ of the sodium chloride solution with $2 \mathrm{~L}$ of the glucose solution is $x \times 10^{-3}$ atm. $x$ is_________________(nearest integer) Solution: (167)...
Read More →The sum of the 4th and the 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44.
Question: The sum of the 4th and the 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the sum of its first 10 terms. Solution: Letabe the first term anddbe the common difference of the AP. $\therefore a_{4}+a_{8}=24$ (Given) $\Rightarrow(a+3 d)+(a+7 d)=24 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow 2 a+10 d=24$ $\Rightarrow a+5 d=12 \quad \cdots(1)$ Also, $\therefore a_{6}+a_{10}=44$ (Given) $\Rightarrow(a+5 d)+(a+9 d)=44 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightar...
Read More →At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of $n$-heptane is 550 mm of Hg.
Question: At $300 \mathrm{~K}$, the vapour pressure of a solution containing 1 mole of $n$-hexane and 3 moles of $n$-heptane is $550 \mathrm{~mm}$ of Hg. At the same temperature, if one more mole of $n$ heptane is added to this solution, the vapour pressure of the solution increases by $10 \mathrm{~mm}$ of $\mathrm{Hg}$. What is the vapour pressure in $\mathrm{mm} \mathrm{Hg}$ of $n$-heptane in its pure state ________________ Solution: (600)...
Read More →Solve the following
Question: If $250 \mathrm{~cm}^{3}$ of an aqueous solution containing $0.73 \mathrm{~g}$ of a protein $\mathrm{A}$ is isotonic with one litre of another aqueous solution containing $1.65 \mathrm{~g}$ of a protein $\mathrm{B}$, at $298 \mathrm{~K}$, the ratio of the molecular masses of $\mathrm{A}$ and $\mathrm{B}$ is______________ $\times 10^{-2}$ (to the nearest integer). Solution: (177) $\pi_{A}=i C_{A} R T, \pi_{B}=i C_{B} R T$ For isotonic solution, $\pi_{A}=\pi_{B}$ $i_{1} C_{1}=i_{2} C_{2}...
Read More →The sum of first n terms of two APs are in the ratio (3n + 8) : (7n + 15).
Question: The sum of firstnterms of two APs are in the ratio (3n+ 8) : (7n+ 15). Find the ratio of their 12th terms. Solution: Let the first term of the first AP beaAnd common difference bed $s_{n}=\frac{n}{2}[2 a+(n-1) d]$ And $a_{n}=a+(n-1) d$ $a_{12}=a+11 d=3 n+8$ Similarly, for second A.P Let first term be $A$ And common difference be $D$ $S_{n}=\frac{n}{2}[2 A+(n-1) D]$ And $A_{n}=A+(n-1) D$ $A_{12}=A+11 D=7 n+15$ We have to find the ratio of 12 th term $\frac{a_{12} \text { of first A.P }}...
Read More →Henry's constant (in kbar) for four gases
Question: Henry's constant (in kbar) for four gases $\alpha, \beta, \gamma$ and $\delta$ in water at $298 \mathrm{~K}$ is given below : (density of water $=10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ at $298 \mathrm{~K}$ ) This table implies that :$\alpha$ has the highest solubility in water at a given pressuresolubility of $\gamma$ at $308 \mathrm{~K}$ is lower than at $298 \mathrm{~K}$The pressure of a $55.5 \mathrm{molal}$ solution of $\gamma$ is $1 \mathrm{bar}$The pressure of a $55.5$ molal solut...
Read More →The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution.
Question: The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution. Which one of the following processes can explain this ?OsmosisDialysisDiffusionReverse osmosisCorrect Option: 1 Solution: It is an example of osmosis. Osmosis is the movement of solvent across a semipermeable membrane towards a higher concentration of solute (concentrated solution)....
Read More →An open beaker of water in equilibrium with water vapour is in a sealed container.
Question: An open beaker of water in equilibrium with water vapour is in a sealed container. When a few grams of glucose are added to the beaker of water, the rate at which water molecules:leaves the vapour increasesleaves the solution increasesleaves the solution decreasesleaves the vapour decreasesCorrect Option: 1 Solution: The vapour pressure of solution will be less than the vapour pressure of pure solvent, so some vapour molecules will get condensed to maintain new equilibrium....
Read More →An AP 5, 12, 19, ... has 50 terms. Find its last term. Hence, find the sum of its last 15 terms.
Question: (i) An AP 5, 12, 19, ... has 50 terms. Find its last term. Hence, find the sum of its last 15 terms. (ii) An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms. Solution: (i) The given AP is 5, 12, 19, ... .Here,a= 5,d= 12 5 = 7 andn= 50.Since there are 50 terms in the AP, so the last term of the AP isa50. $l=a_{50}=5+(50-1) \times 7 \quad\left[a_{n}=a+(n-1) d\right]$ $=5+343$ $=348$ Thus, the last term of the AP is 348.Now,Sum of the last 15 t...
Read More →When 12.2 g of benzoic acid is dissolved in 100 g of water,
Question: When $12.2 \mathrm{~g}$ of benzoic acid is dissolved in $100 \mathrm{~g}$ of water, the freezing point of solution was found to be $-0.93^{\circ} \mathrm{C}\left(\mathrm{K}_{\mathrm{f}}\left(\mathrm{H}_{2} \mathrm{O}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$. The number $(\mathrm{n})$ of benzoic acid molecules associated (assuming $100 \%$ association ) is Solution: (12) n PhCOOH $\rightarrow(\mathrm{PhCOOH})_{\mathrm{n}}$ $N=\frac{1}{X}=\mathrm{i}\{$ As $\quad \a...
Read More →Solve the following
Question: $224 \mathrm{~mL}$ of $\mathrm{SO}_{2}(\mathrm{~g})$ at $298 \mathrm{~K}$ and 1 atm is passed through $100 \mathrm{~mL}$ of $0.1 \mathrm{MNaOH}$ solution. The non-volatile solute produced is dissolved in $36 \mathrm{~g}$ of water. The lowering of vapour pressure of solution (assuming the solution is dilute) $\left(\mathrm{P}_{\left(\mathrm{H}_{2} \mathrm{O}\right)}^{*}=24 \mathrm{~mm}\right.$ of $\mathrm{Hg}$ ) is $\mathrm{x} \times 10^{-2} \mathrm{~mm}$ of Hg, the value of $\mathrm{x}...
Read More →The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41,
Question: The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41, find the sum of its first 15 terms. Solution: Letabe the first term anddbe the common difference of the AP. Then, $a_{16}=5 \times a_{3}$ (Given) $\Rightarrow a+15 d=5(a+2 d) \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow a+15 d=5 a+10 d$ $\Rightarrow 4 a=5 d \quad \ldots(1)$ Also, $a_{10}=41$ (Given) $\Rightarrow a+9 d=41 \quad \ldots(2)$ Solving (1) and (2), we get $a+9 \times \frac{4 a}{5}=41$ $\Rightarrow \fra...
Read More →If a compound AB dissociates to the extent of 75% in an aqueous solution,
Question: If a compound $\mathrm{AB}$ dissociates to the extent of $75 \%$ in an aqueous solution, the molality of the solution which shows a $2.5 \mathrm{~K}$ rise in the boiling point of the solution is_________________ molal. (Rounded-off to the nearest integer) $\left\lceil K_{b}=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$ Solution: (3)...
Read More →The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 10 terms.
Question: The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 10 terms. Solution: Letabe the first term anddbe the common difference of the AP. Then, $a_{13}=4 \times a_{3}$ (Given) $\Rightarrow a+12 d=4(a+2 d) \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow a+12 d=4 a+8 d$ $\Rightarrow 3 a=4 d \quad \ldots(1)$ Also, $a_{5}=16$ (Given) $\Rightarrow a+4 d=16 \quad \ldots$ (2) Solving (1) and (2), we get $a+3 a=16$ $\Rightarrow 4 a=16$ $\Rightarrow a=4$...
Read More →1 molal aqueous solution of an electrolyte
Question: 1 molal aqueous solution of an electrolyte $\mathrm{A}_{2} \mathrm{~B}_{3}$ is $60 \%$ ionised. The boiling point of the solution at 1 atm is__________ $\mathrm{K} .$ (Rounded-off to the nearest integer) $\left[\right.$ Given $\mathrm{K}_{\mathrm{b}}$ for $\left.\left(\mathrm{H}_{2} \mathrm{O}\right)=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$ Solution: (375)...
Read More →Solve the following
Question: $\mathrm{C}_{6} \mathrm{H}_{6}$ freezes at $5.5^{\circ} \mathrm{C}$. The temperature at which a solution of $10 \mathrm{~g}$ of $\mathrm{C}_{4} \mathrm{H}_{10}$ in $200 \mathrm{~g}$ of $\mathrm{C}_{6} \mathrm{H}_{6}$ freeze is__________ ${ }^{\circ} \mathrm{C}$. (The molal freezing point depression constant of $\mathrm{C}_{6} \mathrm{H}_{6}$ is) $5.12^{\circ} \mathrm{C} / \mathrm{m}$ ) Solution: (1)...
Read More →Solve the following
Question: When $9.45 \mathrm{~g}$ of $\mathrm{ClCH}_{2} \mathrm{COOH}$ is added to $500 \mathrm{~mL}$ of water, its freezing point drops by $0.5^{\circ} \mathrm{C}$. The dissociation constant of $\mathrm{ClCH}_{2} \mathrm{COOH}$ is $\mathrm{x} \times 10^{-3}$. The value of $\mathrm{x}$ is _____________(Rounded off to the nearest integer) $\left[K_{f\left(H_{2} O\right)}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$ Solution: (35)...
Read More →Solve the following
Question: When $9.45 \mathrm{~g}$ of $\mathrm{ClCH}_{2} \mathrm{COOH}$ is added to $500 \mathrm{~mL}$ of water, its freezing point drops by $0.5^{\circ} \mathrm{C}$. The dissociation constant of $\mathrm{ClCH}_{2} \mathrm{COOH}$ is $\mathrm{x} \times 10^{-3}$. The value of $\mathrm{x}$ is _____________(Rounded off to the nearest integer) $\left[K_{f\left(H_{2} O\right)}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$ Solution: (35)...
Read More →The sum of first 10 terms of an AP is −150 and the sum of its next 10 terms is −550.
Question: The sum of first 10 terms of an AP is 150 and the sum of its next 10 terms is 550. Find the AP. Solution: Letabe the first term anddbe the common difference of the AP. Then, $S_{10}=-150$ (Given) $\Rightarrow \frac{10}{2}(2 a+9 d)=-150 \quad\left\{S_{n}=\frac{n}{2}[2 a+(n-1) d]\right\}$ $\Rightarrow 5(2 a+9 d)=-150$ $\Rightarrow 2 a+9 d=-30 \quad \ldots(1)$ It is given that the sum of its next 10 terms is 550.Now,S20= Sum of first 20 terms = Sum of first 10 terms + Sum of the next 10 t...
Read More →A solute a dimerizes in water.
Question: A solute a dimerizes in water. The boiling point of a 2 molar solution of A is $100.52^{\circ} \mathrm{C}$. The percentage association of $\mathrm{A}$ is _____________ . (Round off to the Nearest integer) [Use : $\mathrm{K}_{\mathrm{b}}$ for water $=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ Boiling point of water $=100^{\circ} \mathrm{C}$ ] Solution:...
Read More →2 molal solution of a weak acid HA has a freezing point
Question: 2 molal solution of a weak acid HA has a freezing point of $3.885^{\circ} \mathrm{C}$. The degree of dissociation of this acid is ________ $\times 10^{-3}$. (Round off to the Nearest Integer). [Given : Molal depression constant of water = $1.85 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ Freezing point of pure water $\left.=0^{\circ} \mathrm{C}\right]$ Solution: (50) $\Delta \mathrm{T}_{\mathrm{f}}=(1+\alpha) \mathrm{K}_{\mathrm{f}} \mathrm{m}$ $\alpha=0.05=50 \times 10^{-3}$...
Read More →Two APs have the same common difference.
Question: Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms. Solution: Leta1anda2be the first terms of the two APs.Here,a1= 8 anda2= 3Supposedbe the common difference of the two APs. Let $S_{50}$ and $S_{50}^{\prime}$ denote the sums of their first 50 terms. $\therefore S_{50}-S_{50}^{\prime}=\frac{50}{2}\left[2 a_{1}+(50-1) d\right]-\frac{50}{2}\left[2 a_{2}+(50-1) d\right]$ $=25(2 \time...
Read More →Solve the following
Question: A 1 molal $\mathrm{K}_{4} \mathrm{Fe}(\mathrm{CN})_{6}$ solution has a degree of dissociation of $0.4$. Its boiling point is equal to that of another solution which contains $18.1$ weight percent of a non electrolytic solute $\mathrm{A}$. The molar mass of $A$ is___________ u. (Round off to the Nearest Integer). $\left[\right.$ Density of water $\left.=1.0 \mathrm{~g} \mathrm{~cm}^{-3}\right]$ Solution: (85) Effective molality $=0.6+1.6+0.4=2.6 \mathrm{~m}$ For same boiling point, the ...
Read More →The sum of first 7 terms of an AP is 49 and the sum of its first 17 terms is 289.
Question: The sum of first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its firstn terms. Solution: Letabe the first term anddbe the common difference of the given AP.Then we have: $S_{n}=\frac{n}{2}[2 a+(n-1) d]$ $S_{7}=\frac{7}{2}[2 a+6 d]=7[a+3 d]$ $S_{17}=\frac{17}{2}[2 a+16 d]=17[a+8 d]$ However, S7= 49 and S17= 289Now, 7[a+ 3d] = 49⇒a+3d= 7 ...(i)Also, 17[a+ 8d] = 289 ⇒a+ 8d= 17 ...(ii)Subtracting (i) from (ii), we get: 5d= 10⇒d = 2 Puttingd= 2 in (i), ...
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